A207401 Number of n X 6 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.

16, 256, 1296, 4356, 11664, 26896, 55696, 106276, 190096, 322624, 524176, 820836, 1245456, 1838736, 2650384, 3740356, 5180176, 7054336, 9461776, 12517444, 16353936, 21123216, 26998416, 34175716, 42876304, 53348416, 65869456, 80748196

Offset

1,1

Comments

Column 6 of A207403.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (1/9)*n^6 + (4/3)*n^5 + (58/9)*n^4 + (40/3)*n^3 + (49/9)*n^2 - (44/3)*n + 4.

Conjectures from Colin Barker, Jun 22 2018: (Start)

G.f.: 4*x*(4 + 36*x - 40*x^2 + 25*x^3 - 3*x^4 - 3*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

Some solutions for n=4:
..0..0..0..0..0..0....0..0..0..0..0..0....1..1..1..1..1..1....1..0..1..0..1..0
..0..1..0..0..0..0....1..0..1..0..1..0....1..1..1..1..0..1....0..1..0..1..0..0
..0..0..0..0..0..0....0..0..0..0..0..0....1..1..1..1..1..1....0..1..0..1..0..0
..0..0..0..0..0..0....1..0..0..0..0..0....1..1..1..1..0..1....0..1..0..1..0..0

Crossrefs

Cf. A207403.

Sequence in context: A208025 A207805 A016744 * A207750 A207126 A207947

Adjacent sequences: A207398 A207399 A207400 * A207402 A207403 A207404

Keyword

nonn

Author

R. H. Hardin, Feb 17 2012

Status

approved